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Admissible perturbations refer to the perturbations that do not change the Mironenko reflecting function of the system, which are obtained for an autonomous three-dimensional quadratic generalized Langford system with five parameters. The obtained nonautonomous perturbed systems retain many of the qualitative properties of the original system solutions. In particular, the instability (in the sense of Lyapunov) of the equilibrium point, the presence of a periodic solution and its asymptotic stability (instability) are proved for the perturbed systems. The presence of similar chaotic attractors in the original and perturbed systems is shown by numerical simulation.